The Kumaraswamy Gumbel distribution

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose a generalization-referred to as the Kumaraswamy Gumbel distribution-and provide a comprehensive treatment of its structural properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters. We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality of the proposed model. Two bivariate generalizations of the model are proposed.

Computational tools for comparing asymmetric GARCH models via Bayes factors

In this paper we use Markov chain Monte Carlo (MCMC) methods in order to estimate and compare GARCH models from a Bayesian perspective. We allow for possibly heavy tailed and asymmetric distributions in the error term. We use a general method proposed in the literature to introduce skewness into a continuous unimodal and symmetric distribution. For each model we compute an approximation to the marginal likelihood, based on the MCMC output. From these approximations we compute Bayes factors and posterior model probabilities. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

Distribution patterns of a marsh vegetation metacommunity in relation to habitat configuration

The identification of the factors behind the distribution of plant communities in patched habitats may prove useful towards better understanding how ecosystems function. Plant assemblages are especially important for wetland productivity and provide food and habitat to animals. The present study analyses the distribution of a metacommunity of helophytes and phreatophytes in a wetland complex in oder to identify the effects of habitat configuration on the colonisation process. Ponds with wide vegetated shores and a short distance to a big (> 10 ha) wetland, had higher species richness. The average percentage of surface covered by each species in all the wetlands correlated positively with the number of patches occupied by that species. Moreover, the community presented a nested pattern (species-poor patches were subsets of species-rich patches), and this pattern came about by selective extinction and colonisation processes. We also detected the presence of some idiosyncratic species that did not follow nestedness. Conservation managers should attempt to maximise the vegetated shore width and to reduce the degree of isolation to enhance species richness. Furthermore, a single large and poorly isolated reserve may have the highest level of biodiversity in emergent vegetation species in this wetland complex, however, the particular ecological requirements of idiosyncratic species should also be taken into account when managing this type of community.

Generalized beta-generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets. (c) 2011 Elsevier B.V. All rights reserved.

Understanding bias in geographic range size estimates

Aim Estimates of geographic range size derived from natural history museum specimens are probably biased for many species. We aim to determine how bias in these estimates relates to range size. Location We conducted computer simulations based on herbarium specimen records from localities ranging from the southern United States to northern Argentina. Methods We used theory on the sampling distribution of the mean and variance to develop working hypotheses about how range size, defined as area of occupancy (AOO), was related to the inter-specific distribution of: (1) mean collection effort per area across the range of a species (MC); (2) variance in collection effort per area across the range of a species (VC); and (3) proportional bias in AOO estimates (PBias: the difference between the expected value of the estimate of AOO and true AOO, divided by true AOO). We tested predictions from these hypotheses using computer simulations based on a dataset of more than 29,000 herbarium specimen records documenting occurrences of 377 plant species in the tribe Bignonieae (Bignoniaceae). Results The working hypotheses predicted that the mean of the inter-specific distribution of MC, VC and PBias were independent of AOO, but that the respective variance and skewness decreased with increasing AOO. Computer simulations supported all but one prediction: the variance of the inter-specific distribution of VC did not decrease with increasing AOO. Main conclusions Our results suggest that, despite an invariant mean, the dispersion and symmetry of the inter-specific distribution of PBias decreases as AOO increases. As AOO increased, range size was less severely underestimated for a large proportion of simulated species. However, as AOO increased, range size estimates having extremely low bias were less common.

Safety and efficacy of sitaxsentan 50 and 100 mg in patients with pulmonary arterial hypertension

Objective: To assess safety and efficacy of sitaxsentan 50 and 100 mg in patients with pulmonary arterial hypertension (PAH). Background: Sitaxsentan is a highly selective endothelin-A receptor antagonist that was recently withdrawn by the manufacturer because of a pattern of idiosyncratic liver injury. Methods: Before sitaxsentan withdrawal, this 18-week double-blind, placebo-controlled study randomized patients with PAH to receive placebo or sitaxsentan 50 or 100 mg once daily. The primary efficacy endpoint was change from baseline in 6-min walk distance (6MWD) at week 18. Changes in World Health Organization (WHO) functional class and time to clinical worsening (TTCW) were secondary endpoints. The primary efficacy analysis was powered for sitaxsentan 100 mg versus placebo. Results: Of 98 randomized patients, 61% were WHO functional class II at baseline. Improvement from baseline to week 18 in 6MWD occurred with sitaxsentan 100 but not 50 mg; a strong placebo effect was observed. At week 18, WHO functional class was improved or maintained in more patients receiving sitaxsentan 100 mg than placebo (P = 0.038); 0% versus 12% of patients deteriorated, respectively. TTCW was not significantly different for 100-mg sitaxsentan patients than placebo (P = 0.090). Adverse events (AEs) occurring more frequently with sitaxsentan (50 or 100 mg) included headache, peripheral edema, dizziness, nausea, extremity pain, and fatigue; most AEs were of mild or moderate severity. Conclusion: Sitaxsentan 100 mg improved functional class but not 6MWD in PAH patients who were mostly WHO functional class II at baseline. No patient receiving sitaxsentan 100 mg experienced clinical worsening; sitaxsentan was well tolerated. (C) 2011 Elsevier Ltd. All rights reserved.

A quantitative approach to evolution of music and philosophy

The development of new statistical and computational methods is increasingly making it possible to bridge the gap between hard sciences and humanities. In this study, we propose an approach based on a quantitative evaluation of attributes of objects in fields of humanities, from which concepts such as dialectics and opposition are formally defined mathematically. As case studies, we analyzed the temporal evolution of classical music and philosophy by obtaining data for 8 features characterizing the corresponding fields for 7 well-known composers and philosophers, which were treated with multivariate statistics and pattern recognition methods. A bootstrap method was applied to avoid statistical bias caused by the small sample data set, with which hundreds of artificial composers and philosophers were generated, influenced by the 7 names originally chosen. Upon defining indices for opposition, skewness and counter-dialectics, we confirmed the intuitive analysis of historians in that classical music evolved according to a master apprentice tradition, while in philosophy changes were driven by opposition. Though these case studies were meant only to show the possibility of treating phenomena in humanities quantitatively, including a quantitative measure of concepts such as dialectics and opposition, the results are encouraging for further application of the approach presented here to many other areas, since it is entirely generic.

Likelihood-based inference for power distributions

This paper considers likelihood-based inference for the family of power distributions. Widely applicable results are presented which can be used to conduct inference for all three parameters of the general location-scale extension of the family. More specific results are given for the special case of the power normal model. The analysis of a large data set, formed from density measurements for a certain type of pollen, illustrates the application of the family and the results for likelihood-based inference. Throughout, comparisons are made with analogous results for the direct parametrisation of the skew-normal distribution.